Make particles start their animations when they're emitted using Animation Nodes?
It has basically three steps:

1) Transform of the objects at the particle location. 

2) Delay the shape key of individual objects based on the birth time i.e., shape key animation starts when the particle is born.

3) Then making objects visible only when they are alive.

============================================

Single Object:

Here is the complete note-tree:  



Blend File: 



============================================

Multiple Objects:

1) Here I have made a Group-Node which gives the instance amount per objects (say multiple ships) by keeping the total is equal to the total number of particles. We will use these amounts in the instancer node to generates the instances of the individual objects (or ships).

2) Here is the setup to instance individual objects (or ships),


3) Complete node-tree:


Blend File:



============================================

Multiple Objects with different materials:

For this, you need to install Animation Nodes + Extra Nodes which has the Material Instancer Node and Material Attribute Output node,



Blend File: 

 

============================================

Multiple Objects with animated materials:



Blend File: